P Value in Hypothesis Testing Calculator

Calculator

Test type

Input mode

Tail direction

Alpha

Test statistic

DF 1

DF 2

Sample mean

Null mean

Standard deviation

Mean test sample size

Sample variance

Hypothesized variance

Variance test sample size

Numerator variance

Denominator variance

Example Data Table

Case	Test	Statistic	Degrees of Freedom	Tail	Alpha	Typical Use
1	Z	1.96	N/A	Two tailed	0.05	Known standard deviation
2	T	2.15	24	Right tailed	0.05	Small sample mean test
3	Chi square	30.5	18	Right tailed	0.01	Variance test
4	F	2.40	8, 12	Right tailed	0.05	Variance ratio test

Formula Used

Z test: z = (x̄ - μ0) / (σ / √n). The p value comes from the standard normal distribution.

T test: t = (x̄ - μ0) / (s / √n). Degrees of freedom are n - 1 for a one sample mean test.

Chi square test: χ² = (n - 1)s² / σ0². Degrees of freedom are n - 1.

F test: F = s1² / s2². The numerator and denominator use separate degrees of freedom.

Tail conversion: left p = CDF, right p = 1 - CDF, and two tailed p = 2 × min(CDF, 1 - CDF).

How to Use This Calculator

Select the test distribution that matches your hypothesis test.
Choose direct statistic mode or sample summary mode.
Enter the statistic, degrees of freedom, or summary values.
Select the correct left, right, or two tailed option.
Enter alpha, then press Calculate.
Review the p value and decision statement.
Use CSV or PDF download when you need a saved copy.

Understanding P Values in Hypothesis Testing

P values help you judge evidence against a null hypothesis. They do not prove that a claim is true. They measure how unusual your statistic is when the null model is assumed. A small value means the observed result would be rare under that model. A large value means the data is not unusual enough to reject the null claim.

Choosing the Correct Test

This calculator supports common test families used in statistics. Use the z option when the population standard deviation is known or the sample is large. Use the t option for sample mean tests with an estimated standard deviation. Use the chi square option for variance tests. Use the F option when comparing two variances or using an F statistic from analysis work.

Tail Direction

The tail choice is important. A left tailed test looks for unusually small statistics. A right tailed test looks for unusually large statistics. A two tailed test checks both directions. Your research question should decide the tail before you view the result. Changing the tail after seeing data can make a conclusion misleading.

Alpha and Decisions

The alpha value is your rejection rule. Common choices are 0.10, 0.05, and 0.01. If the p value is less than or equal to alpha, the calculator marks the result as statistically significant. This means you reject the null hypothesis. It does not measure practical importance. Always compare the result with sample size, design quality, and subject knowledge.

Input Modes

Summary input mode helps when you have raw study values. It calculates the statistic from sample means, variances, sample size, and degrees of freedom. Direct statistic mode is useful when your textbook, software, or exam question already gives the test statistic. Both modes lead to the same p value when the inputs match.

Saving Your Work

Use the download buttons to save your work. The CSV file is useful for spreadsheets. The PDF file is useful for reports, homework, and record keeping. Keep notes about assumptions, tail direction, and alpha with every result. That habit makes your statistical decision easier to audit later. Remember that statistical significance is not certainty. Outliers, biased sampling, and weak measurement can affect every test. When assumptions are doubtful, treat the result as a guide, then review data carefully before making decisions.

FAQs

What is a p value?

A p value is the probability of getting a result at least as extreme as your observed statistic, assuming the null hypothesis is true.

Does a small p value prove the alternative hypothesis?

No. It only shows that the observed result is unlikely under the null model. Study design and assumptions still matter.

Which alpha value should I use?

Common alpha values are 0.10, 0.05, and 0.01. Choose alpha before testing. Use stricter values when false positives are costly.

When should I use a two tailed test?

Use a two tailed test when results in either direction would be important. Decide this before looking at sample results.

What is the difference between z and t tests?

A z test often uses a known population standard deviation. A t test uses sample standard deviation and degrees of freedom.

Can I use this for chi square variance tests?

Yes. Select the chi square option. Enter the statistic and degrees of freedom, or use summary values for variance testing.

Why does the F test need two degrees of freedom?

The F distribution compares two variance estimates. Each estimate has its own degrees of freedom, so both are required.

What should I report with a p value?

Report the test type, statistic, degrees of freedom, tail direction, alpha, p value, and your decision about the null hypothesis.